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The image below shows the performance of Vanguard Total Stock Market ETF (NYSE Arca: VTI). I cannot understand how $10,000 becomes $34,070 after 10 years with a 10-year return of 12.80%.

Shouldn't it be $10,000 * 1.128 = $11,280 ?

Is some kind of compounding happening here? What's the equation?

VTI performance

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I cannot understand how $10,000 becomes $34,070 after 10 years with a 10-year return of 12.80%.

12.80% is the compound annual growth rate (CAGR). It is 12.80% every year for 10 years.

\sqrt[10]{\frac{34070}{10000}} \approx 1.13

Shouldn't it be $10,000 * 1.128 = $11,280 ?

No. It should be 10000(1.128^{10}) \approx 33350

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  • Does it mean I need to re-invest the profits back into ETF to make it reach $33k. Or does it mean that the VTI grows 12.8% per year and if I just sit on it for 10 years it will become $33k. I googled "CAGR" and investopedia says "assuming the profits were reinvested at the end of each year of the investment’s lifespan" in this link here investopedia.com/terms/c/cagr.asp
    – user855
    Nov 1, 2020 at 2:03
  • @user855 By "re-invest the profits", do you mean reinvesting the dividends?
    – Flux
    Nov 1, 2020 at 2:08
  • I have no clue about this. That Investopedia website was using those words. I really just want to know if I buy VTI (say $10k worth) now, what else do I need to do each year so that it becomes $34k in 10 years. Do nothing else? Or do I need to "reinvest" as this article is claiming I need to do?
    – user855
    Nov 1, 2020 at 2:12
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    @user855 If the performance numbers on Vanguard's website include dividend reinvestment (i.e. "total return"), then you would have had to reinvest all dividends to reach $34,070. If the numbers do not include dividend reinvestment (i.e. "price return"), then you would not have had to reinvest your dividends to reach $34,070.
    – Flux
    Nov 1, 2020 at 2:18
  • @user855 I have no idea whether or not Vanguard's numbers assume dividend reinvestment. You can check with them.
    – Flux
    Nov 1, 2020 at 2:19

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